Many important practical & mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use & how we should use them.
Which comparing strategies work best in which situations?
Notes
Vocabulary= proportion is a statement about equivalent ratios or fractions
Example- ½ = 2/4
Method= using proportions. Like this-
½ = x/4
& I want to find x. I used this method to solve the problems in 6.3
United States
248,710
192,726
55,984
199,686
29,986
22,354
1959
7274
New England
13,207
10,598
2609
12,033
628
568
33
232
Middle Atlantic
37,602
34,193
3409
30,036
4986
3186
92
1104
East North Central
42,009
32,557
9452
35,764
4817
1438
150
573
West North Central
17,660
10,132
7528
16,254
899
289
188
195
South Atlantic
43,567
32,461
11,106
33,391
8924
2133
172
631
East South Central
15,176
8513
6663
12,049
2977
95
41
84
West South Central
26,703
19,614
7,089
20,142
3929
4539
350
407
Pacific
39,127
35,479
3648
28,255
2454
8114
453
3831
Mountain
13,659
9179
4480
11,762
374
1992
481
217
A.How many of the 1000 delegates should be chosen from each of the nine geographic regions?
I used a table to answer this question & I also used proportions.
# Of people that should be chosen from each of the nine geographic regions
New England
53 delegates
13207000/248710000= ?/1000
Middle Atlantic
151 delegates
37602000/248710000= ?/1000
East North Central
168 delegates
420090000/248710000= ?/1000
West North Central
71 delegates
17660000/248710000= ?/1000
South Atlantic
175 delegates
43567000/248710000= ?/1000
East South Central
61 delegates
15176000/248710000= ?/1000
West South Central
107 delegates
26703000/248710000= ?/1000
Mountain
54 delegates
13659000/248710000= ?/1000
Pacific
157 delegates
39127000/248710000= ?/1000
B.How many of the 1000 delegates should be from metropolitan areas, and how many should be from rural areas?
I solved this problem by using a proportion.
Metropolitan population/US Population = # of delegates from metropolitan areas/# of delegates
This is the same as =
19726000/248710000= ?/1000
To get ? I cross-multiplied 1000 by 192726000. Then I divided the product by 248710000 I got the answer for ?.
19726000 x 1000 = 192726000000
192726000000 divided by 248710000= 775
So 775 delegates should be from the metropolitan area.
To how many delegates should be from the rural area I subtracted the total # of delegates by the delegates that should be from the metropolitan areas.
1000 – 775 = 225.
So 225 people should be from the rural areas.
C.How many of the delegates should be of Hispanic origin?
To solve this problem I used the same method from problem B.
Hispanic population/US population = # of Hispanic delegates/ # of delegates
This is the same as=
22354000/248710000 = ?/1000
To get ? I cross-multiplied 1000 by 22354000. Then I divided the product by 248710000 I got the answer for ?.
22354000 x 1000 = 22354000000
22354000000 divided by 248710000= 90
So 90 delegates should be of Hispanic origin.
D.Four racial groups are named in the data: white; black; Native American-Eskimo-Aleut; & Asian-Pacific Islanders. How many of the total 1000 delegates should represent each of these races? How many should represent the category “all other races” (which is not mentioned in the data)?
I used the same method from Problem C to solve this problem.
White
802 delegates
199686000/248710000= ?/1000
Black
120 delegates
29986000/248710000= ?/1000
Native American/Eskimo/Aleut
8 delegates
1959000/248710000= ?/1000
Asian/Pacific Islander
29 delegates
7274000/248710000= ?/1000
All other races
41 delegates
1000 - 959
E.Use your answers to A-D to help you develop a plan for selecting the delegates. Describe your plan in a report that you could submit to the conference organizers.
I think 53 people should be from New England, 151 people from Middle Atlantic, 168 people from East North Central, 71 people from West North Central, 175 from South Atlantic, 61 from East South Central, 107 people from West South Central, 54 people from Mountain & 157 from Pacific. I believe 775 people of the delegates should be from Metropolitan areas & 225 of the delegates should be from rural areas. Also according to the calculations there should be 802 white delegates, 120 black delegates, 8 Native American/Eskimo/Aleut delegates, 29 Asian/Pacific Islander delegates & 41 delegates from other races.
Follow-Up If you could add another criterion to help choose the delegates so that the representation would be fair, what criterion would you add & why?
I would add immigrants/foreign people because lots of people who live in the U.S are from other countries
JSP
Many important practical & mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use & how we should use them.
Which comparing strategies work best in which situations?
Notes
Vocabulary= proportion is a statement about equivalent ratios or fractions
Example- ½ = 2/4
Method= using proportions. Like this-
½ = x/4
& I want to find x. I used this method to solve the problems in 6.3
A. How many of the 1000 delegates should be chosen from each of the nine geographic regions?
I used a table to answer this question & I also used proportions.
# Of people that should be chosen from each of the nine geographic regions
B. How many of the 1000 delegates should be from metropolitan areas, and how many should be from rural areas?
I solved this problem by using a proportion.
Metropolitan population/US Population = # of delegates from metropolitan areas/# of delegates
This is the same as =
19726000/248710000= ?/1000
To get ? I cross-multiplied 1000 by 192726000. Then I divided the product by 248710000 I got the answer for ?.
19726000 x 1000 = 192726000000
192726000000 divided by 248710000= 775
So 775 delegates should be from the metropolitan area.
To how many delegates should be from the rural area I subtracted the total # of delegates by the delegates that should be from the metropolitan areas.
1000 – 775 = 225.
So 225 people should be from the rural areas.
C. How many of the delegates should be of Hispanic origin?
To solve this problem I used the same method from problem B.
Hispanic population/US population = # of Hispanic delegates/ # of delegates
This is the same as=
22354000/248710000 = ?/1000
To get ? I cross-multiplied 1000 by 22354000. Then I divided the product by 248710000 I got the answer for ?.
22354000 x 1000 = 22354000000
22354000000 divided by 248710000= 90
So 90 delegates should be of Hispanic origin.
D. Four racial groups are named in the data: white; black; Native American-Eskimo-Aleut; & Asian-Pacific Islanders. How many of the total 1000 delegates should represent each of these races? How many should represent the category “all other races” (which is not mentioned in the data)?
I used the same method from Problem C to solve this problem.
E. Use your answers to A-D to help you develop a plan for selecting the delegates. Describe your plan in a report that you could submit to the conference organizers.
I think 53 people should be from New England, 151 people from Middle Atlantic, 168 people from East North Central, 71 people from West North Central, 175 from South Atlantic, 61 from East South Central, 107 people from West South Central, 54 people from Mountain & 157 from Pacific. I believe 775 people of the delegates should be from Metropolitan areas & 225 of the delegates should be from rural areas. Also according to the calculations there should be 802 white delegates, 120 black delegates, 8 Native American/Eskimo/Aleut delegates, 29 Asian/Pacific Islander delegates & 41 delegates from other races.
Follow-Up
If you could add another criterion to help choose the delegates so that the representation would be fair, what criterion would you add & why?
I would add immigrants/foreign people because lots of people who live in the U.S are from other countries